Show that the angle between the diagonal of a cube is `cos^(-1)((1)/(3))`.

The angle between the two diagonals of a cube is .....

The edge of a cube is of length of a. The shortest distance between the diagonals of a cube an edge skew to it is ........

Show that the tangent of an angle between the lines (x)/(a) + (y)/( b) = 1 and (x)/( a) - (y)/( b) = 1 is (2 ab)/( a^(2) - b^(2) ) .

(i) Find the angle bewteen the lines whose direction ratios are 1, 2, 3 and - 3 , 2 , 1 (ii) Find the angle between two diagonals of a cube.

If the lines ax^2+2hxy+by^2=0 be two sides of a parallelogram and the line lx+my=1 be one of its diagonal, show that the equation of the other diagonal is y (bl-hm)=x(am-hl).

A line makes the angle alpha, beta , gamma and delta with the diagonals of a cube. The cos^2 alpha + cos^2 beta + cos^2 gamma + cos^2 delta =.............

If one of the lines of my^2+(1-m^2)xy-mx^2=0 is a bisector of the angle between lines xy=0 , then cos ^(-1) (m) is

A line makes angles alpha, beta, gamma and delta with the diagonals of a cube, prove that sin^(2) alpha + sin^(2) beta + sin^(2) gamma + sin^(2) delta = (8)/(3) .

The slope of a line is double of the slope of another line. If tangent of the angle between them is (1)/(3) , find the slopes of the lines.